Rozwiązanie równania:
[tex](x-3)(x+3)-(x-3)^2-(x+2)^2=-25\\\\x^2-3^2-(x^2-2\cdot x\cdot3+3^2)-(x^2+2\cdot x\cdot2+2^2)=-25\\\\x^2-9-(x^2-6x+9)-(x^2+4x+4)=-25\\\\x^2-9-x^2+6x-9-x^2-4x-4=-25\\\\-x^2+2x-22+25=0\\\\-x^2+2x+3=0\\\\a=-1, \ b=2, \ c=3 \ (z \ postaci \ y=ax^2+bx+c)\\\\\Delta=2^2-4\cdot(-1)\cdot3=4+12=16\\\\x_1=\frac{-2-\sqrt{16}}{2\cdot(-1)}=\frac{-2-4}{-2}=\frac{-6}{-2}=\boxed3\\\\x_2=\frac{-2+\sqrt{16}}{2\cdot(-1)}=\frac{-2+4}{-2}=\frac{2}{-2}=\boxed{-1}[/tex]
Użyte wzory:
[tex](a-b)(a+b)=a^2-b^2\\\\(a-b)^2=a^2-2ab+b^2\\\\(a+b)^2=a^2+2ab+b^2[/tex]
[tex]\Delta=b^2-4ac[/tex]
[tex]x_1=\frac{-b-\sqrt{\Delta}}{2a}\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}[/tex]